In the Sun there has been much progress towards answering fundamental problems with profound implications for the behaviour of cosmic magnetic fields in other stars. A review is given here of such problems, including identifying some of the outstanding questions that remain. In the solar interior, the main dynamo operates at the base of the convection zone, but its details have not been identified. In the solar surface, recent observations have revealed many new and surprising properties of magnetic fields, but understanding the key processes of flux emergence, fragmentation, merging and cancellation is rudimentary. Sunspots have until very recently been an enigma. In the atmosphere, there are many new ideas for coronal heating and solar wind acceleration, but the mechanisms have not yet been pinned down. Also, the detailed mechanisms for solar flares and coronal mass ejections remain controversial. In future, new generations of space and ground-based measurements and computational modelling should enable a definitive physical understanding of these puzzles.

Sunspot fine structure has been modeled in the past by a combination of idealized magneto-convection simulations and simplified models that prescribe the magnetic field and flow structure to a large degree. Advancement in numerical methods and computing power has enabled recently 3D radiative MHD simulations of entire sunspots with sufficient resolution to address details of umbral dots and penumbral filaments. After a brief review of recent developments we focus on the magneto-convective processes responsible for the complicated magnetic structure of the penumbra and the mechanisms leading to the driving of strong horizontal outflows in the penumbra (Evershed effect). The bulk of energy and mass is transported on scales smaller than the radial extent of the penumbra. Strong horizontal outflows in the sunspot penumbra result from a redistribution of kinetic energy preferring flows along the filaments. This redistribution is facilitated primarily through the Lorentz force, while horizontal pressure gradients play only a minor role. The Evershed flow is strongly magnetized: While we see a strong reduction of the vertical field, the horizontal field component is enhanced within filaments.

In this paper we summarize the studies of flare-related changes of photospheric magnetic fields. When vector magnetograms are available, we always find an increase of transverse field at the polarity inversion line (PIL). We also discuss 1 minute cadence line-of-sight MDI magnetogram observations, which usually show prominent changes of magnetic flux contained in the flaring δ spot region. The observed limb-ward flux increases while disk-ward flux decreases rapidly and irreversibly after flares. These observations provides evidences, either direct or indirect, for the theory and prediction of Hudson, Fisher & Welsch (2008) that the photospheric magnetic fields would respond to coronal field restructuring and turn to a more horizontal state near the PIL after eruptions. From the white-light observations, we find that at flaring PIL, the structure becomes darker after an eruption, while the peripheral penumbrae decay. Using high-resolution Hinode data, we find evidence that only dark fibrils in the “uncombed” penumbral structure disappear while the bright grains evolve to G-band bright points after flares.

Helicity measures complexity in the field. Magnetic helicity is given by a volume integral over the scalar product of magnetic field B and its vector potential A. A direct computation of magnetic helicity in the solar atmosphere is not possible due to unavailability of the observations at different heights and also due to non-uniqueness of A. The force-free parameter α has been used as a proxy of magnetic helicity for a long time. We have clarified the physical meaning of α and its relationship with the magnetic helicity. We have studied the effect of polarimetric noise on estimation of various magnetic parameters. Fine structures of sunspots in terms of vertical current (Jz) and α have been examined. We have introduced the concept of signed shear angle (SSA) for sunspots and established its importance for non force-free fields. We find that there is no net current in sunspots even in presence of a significant twist, showing consistency with their fibril-bundle nature. The finding of existence of a lower limit of SASSA for a given class of X-ray flare will be very useful for space weather forecasting. A good correlation is found between the sign of helicity in the sunspots and the chirality of the associated chromospheric and coronal features. We find that a large number of sunspots observed in the declining phase of solar cycle 23 do not follow the hemispheric helicity rule whereas most of the sunspots observed in the beginning of new solar cycle 24 do follow. This indicates a long term behaviour of the hemispheric helicity patterns in the Sun. The above sums up my PhD thesis.

The most promising model for explaining the origin of solar magnetism is the flux transport dynamo model, in which the toroidal field is produced by differential rotation in the tachocline, the poloidal field is produced by the Babcock–Leighton mechanism at the solar surface and the meridional circulation plays a crucial role. After discussing how this model explains the regular periodic features of the solar cycle, we come to the questions of what causes irregularities of solar cycles and whether we can predict future cycles. Only if the diffusivity within the convection zone is sufficiently high, the polar field at the sunspot minimum is correlated with strength of the next cycle. This is in conformity with the limited available observational data.

An assessment on the capabilities of modern spectropolarimeters and magnetographs is in order since most of our astrophysical results rely upon the accuracy of the instrumentation and on the sensitivity of the observables to variations of the sought physical parameters. A contribution to such an assessment will be presented in this talk where emphasis will be made on the use of the so-called response functions to gauge the probing capabilities of spectral lines and on an analytical approach to estimate the uncertainties in the results in terms of instrumental effects. The Imaging Magnetograph eXperiment (IMaX) and the Polarimetric and Helioseismic Imager (PHI) will be used as study cases.

Recent observations of coronal loops in solar active regions show that their heating must be a truly dynamic process. Even though it seems clear that the energy source is the magnetic field that confines the coronal plasma, the details of how it dissipates are still a matter of debate. In this presentation we review the theoretical models of coronal heating, which have been traditionally clasified as DC or AC depending on the electrodynamic response of the loops to the photospheric driving motions.

Also, we show results from numerical simulations of the internal dynamics of coronal loops within the framework of the reduced MHD approximation. These simulations indicate that the application of a stationary velocity field at the photospheric boundary leads to a turbulent stationary regime after several photospheric turnover times. Once this turbulent regime is set, both DC and AC stresses dissipate at faster rates as a result of a direct energy cascade.

The automated detection of solar features is a technique which is relatively underused but if we are to keep up with the flow of data from spacecraft such as the recently launched Solar Dynamics Observatory, then such techniques will be very valuable to the solar community. Automated detection techniques allow us to examine a large set of data in a consistent way and in relatively short periods of time allowing for improved statistics to be carried out on any results obtained. This is particularly useful in the field of sunspot study as catalogues can be built with sunspots detected and tracked without any human intervention and this provides us with a detailed account of how various sunspot properties evolve over time. This article details the use of the Sunspot Tracking And Recognition Algorithm (STARA) to create a sunspot catalogue. This catalogue is then used to analyse the magnetic fields in sunspot umbrae from 1996-2010, taking in the whole of solar cycle 23.

The best way to test the stellar magnetic field mapping codes is to apply them, with some changes, to the Sun, where high-precision disk-integrated and disk-resolved observations are available for a long time. Data sets of the full-disk magnetograms and the solar mean magnetic fields (SMMF) measurements are provided, for example, by the J.M.Wilcox Solar observatory (WSO) and by the Sayan Solar observatory (SSO). In the second case the measurements in the Stokes-meter mode simultaneously in many spectral lines are available. This study is devoted to analysis of the SSO quasi-simultaneous full-disk magnetograms and SMMF measurements. Changes of the SMMF signal with rotation of the surface large-scale magnetic fields are demonstrated. Besides, by deleting of selected pixels with active regions (AR) from the maps their contribution to the integrated SMMF signal is evaluated. It is shown that in some cases the role of AR can be rather significant.

I make a perhaps slightly foolhardy attempt to synthesize a semi-coherent scenario relating cycle characteristics, starspots, and the underlying magnetic fields with stellar properties such as mass and rotation. Key to this attempt is to first study single dwarfs; differential rotation plays a surprising role.

The evolution of stellar activity involves a complex interplay between the interior dynamo mechanism, the emergent magnetic field configurations and their coupling with stellar winds, the subsequent angular momentum evolution, and fundamental stellar parameters. The discussion of the evolution of surface activity will emphasize the main sequence phase, from the ZAMS to stars of solar-age. We will focus particularly on the evolution of the fractional area coverages of spots on the surfaces of solar-type stars. We fit an empirical relation to the fractional mean spot area coverage as a function of age for ages greater than the Pleiades of the form log(MeanSpotCoverage) = 0.90(±0.26) − 1.03(±0.10)log(Age), where Age is in Myr. In addition, we summarize the relative evolution of radiative emissions in various short wavelength bands that are associated with stellar magnetic field-related activity. Possible effects on young planetary atmospheres also are appropriate to consider given that stellar surface activity is the origin of the high-energy component of the ambient radiation and particle fields in which planetary atmosphere evolution occurs.

We present a 30 year compilation of V-band differential photometry for the Pleiades K dwarf HII 1883. HII 1883 has an average rotational period 〈Prot〉 of ~0.235d and displays rotational modulation due to non-uniform surface brightness as large as 0.2 magnitudes in V. Preliminary work yields a cycle period of ~9yrs and rotational shear δProt/〈Prot〉 considerably less than solar. With such a long baseline of data available we can explore many aspects of the star's photometric variability. We present studies of the variation of the rotational modulation amplitude, 〈V〉, and Prot over the cycle.

The Kepler satellite provides a unique opportunity to study the detailed optical photometric variability of late-type stars with unprecedentedly long (several year) continuous monitoring and sensitivity to very small-scale variations. We are studying a sample of over two hundred cool (mid-A - late-K spectral type) stars using Kepler long-cadence (30 minute sampling) observations. These stars show a remarkable range of photometric variability, but in this paper we concentrate on rotational modulation due to starspots and flaring. Modulation at the 0.1% level is readily discernable. We highlight the rapid timescales of starspot evolution seen on solar-like stars with rotational periods between 2 and 7 days.

While the rising flux tube paradigm is an elegant theory, its basic assumptions, thin flux tubes at the bottom of the convection zone with field strengths two orders of magnitude above equipartition, remain numerically unverified at best. As such, in recent years the idea of a formation of sunspots near the top of the convection zone has generated some interest. The presence of turbulence can strongly enhance diffusive transport mechanisms, leading to an effective transport coefficient formalism in the mean-field formulation. The question is what happens to these coefficients when the turbulence becomes anisotropic due to a strong large-scale mean magnetic field. It has been noted in the past that this anisotropy can also lead to highly non-diffusive behavior. In the present work we investigate the formation of large-scale magnetic structures as a result of a negative contribution of turbulence to the large-scale effective magnetic pressure in the presence of stratification. In direct numerical simulations of forced turbulence in a stratified box, we verify the existence of this effect. This phenomenon can cause formation of large-scale magnetic structures even from initially uniform large-scale magnetic field.

The photospheric spot activity of some of the stars with transiting planets discovered by the CoRoT space experiment is reviewed. Their out-of-transit light modulations are fitted by a spot model previously tested with the total solar irradiance variations. This approach allows us to study the longitude distribution of the spotted area and its variations versus time during the five months of a typical CoRoT time series. The migration of the spots in longitude provides a lower limit for the surface differential rotation, while the variation of the total spotted area can be used to search for short-term cycles akin the solar Rieger cycles. The possible impact of a close-in giant planet on stellar activity is also discussed.

During the eclipse of a planet, spots and other features on the surface of the host star may be occulted. This will cause small variations in the light curve of the star. Detailed studies of these variations during planetary transits provide a wealth of information about the starspots properties such as size, position, temperature (i.e. intensity), and magnetic field. If observation of multiple transits is available, the spots lifetime can be estimated. Moreover it may also be possible to determine the stellar rotation and whether differential rotation is present. Here, the study is performed using a method that simulates the passage of a planet (dark disk) in front of a star with multiple spots of different sizes, intensities, and positions on its surface. The data variations in the light curve of the star are fit using this method, yielding the starspots properties. Results are presented for solar-like stars, such as the active star CoRoT-2a.

Systematic efforts of monitoring starspots from the middle of the XXth century, and the results obtained from the datasets, are summarized with special focus on the observations made by automated telescopes. Multicolour photometry shows correlations between colour indices and brightness, indicating spotted regions with different average temperatures originating from spots and faculae. Long-term monitoring of spotted stars reveals variability on different timescales.

On the rotational timescale new spot appearances and starspot proper motions are followed from continuous changes of light curves during subsequent rotations. Sudden interchange of the more and less active hemispheres on the stellar surfaces is the so called flip-flop phenomenon. The existence and strength of the differential rotation is seen from the rotational signals of spots being at different stellar latitudes.

Long datasets, with only short, annual interruptions, shed light on the nature of stellar activity cycles and multiple cycles. The systematic and/or random changes of the spot cycle lengths are discovered and described using various time-frequency analysis tools. Positions and sizes of spotted regions on stellar surfaces are calculated from photometric data by various softwares. From spot positions derived for decades, active longitudes on the stellar surfaces are found, which, in case of synchronized eclipsing binaries can be well positioned in the orbital frame, with respect to, and affected by, the companion stars.

A-type stars have both a near-surface layer of fast convection that can excite acoustic modes and a deep zone of core convection whose properties may be probed with asteroseismology. Many A-type stars also exhibit large magnetic spots that are often attributed to surviving primordial fields of global scale in the intervening radiative zone. We have explored the potential for core convection in rotating A-type stars to build strong magnetic fields through dynamo action. These 3-D simulations using the ASH code provide guidance on the nature of differential rotation and magnetic fields that may be present in the deep interiors of these stars, thus informing the asteroseismic deductions now becoming feasible. Our models encompass the inner 30% by radius of a two solar mass A-type star, rotating at four times the solar rate and capturing the convective core and a portion of the overlying radiative envelope. Convection in these stars drives a strong retrograde differential rotation and yields a core that is prolate in shape. When dynamo action is admitted, the convection generates strong magnetic fields largely in equipartition with the dynamics. Remarkably, introducing a modest but large-scale external field threading the radiative envelope (which may be of primordial origin) can substantially alter the turbulent dynamics of the convective interior. The resulting convection involves a complex assembly of helical rolls that link distant portions of the core and stretch and advect magnetic field, ultimately yielding magnetic fields of super-equipartition strength.

Our recent studies of late B-type stars with HgMn peculiarity revealed for the first time the presence of fast dynamical evolution of chemical spots on their surfaces. These observations suggest a hitherto unknown physical process operating in the stars with radiative outer envelopes. Furthermore, we have also discovered existence of magnetic fields on these stars that have up to now been thought to be non-magnetic. Here we will discuss the dynamical spot evolution on HD 11753 and our new results on magnetic fields on AR Aur.

V889 Herculis is one of the brightest single early-G type stars, a young Sun, that is rotating fast enough (Prot =1.337 days) for mapping its surface by Doppler Imaging. The 10 FOCES spectra collected between 13-16 Aug 2006 at Calar Alto Observatory allowed us to reconstruct one single Doppler image for two mapping lines. The Fe i-6411 and Ca i-6439 maps, in a good agreement, revealed an asymmetric polar cap and several weaker features at lower latitudes. Applying the sheared-image method with our Doppler reconstruction we perform an investigation to detect surface differential rotation (DR). The resulting DR parameter, δΩ/Ω≈0.009 of solar type, is compared to previous studies which reported either much stronger shear or comparably weak DR, or just preferred rigid rotation. Theoretical aspects are also considered and discussed.